LOADING ANALYSIS FOR A REINFORCED CONCRETE DECK SLAB- EXAMPLE

Determine the positive moment to be used in the design of the deck slab of an ordinary simple span bridge as shown. 

Materials used are the following:
Slab:                   Normal weight concrete, f'c = 35 MPa
Wearing surface:   Asphalt concrete
Thickness of future wearing surface:         60mm
Thickness of top integral wearing surface: 12mm

Given as an ordinary bridge, the load modifier, = 1.0. 

Assuming that we are going to use #36 bars:

     Top cover           = 40mm

     Bottom cover      = 25mm

Using Normal weight concrete (f'c = 35 MPa), 

                                              ' or taking the unit weight,

                                        

Future wearing surface uses Asphalt concrete:
                                    or using the unit weight: 

                                               


So let's start computing for DW and DC. In order to solve for the dead loads, the dimensions of the bridge should be identified first.


1. For the overhang width, using 50% of S:

                  

2. For the thickness of the slab (overall depth) and overhang: (simple span)

Bridge Design and Evaluation LRFD and LRFR

So considering the design depth for the concrete slab:

Design depth =  overall depth - sacrifical surface= 250mm -12mm=238mm

With bridge dimensions complete, we can compute for DW and DC (using 1m strip).

1. Solve for DW:

It should be noted that since the future wearing surface is much thicker than the integrated thickness, DW should account for the FWS.

                                


                               

2. Solve for DC of parapet:

                             


                            

So, computing for DC of parapet:


                              

                             

3. Solve for DC of slab. There are different parameters which should be considered for the DW of slab such as:

• Weight of the slab
• Miscellaneous (railings, lighting, etc) 
• Stay in place formworks

a. For DC of slab:

                           

                          
                       
                         

b. For miscellaneous DC, let's take 5% of the slab weight:

                                              
                     

c. For Stay-in-place formworks, the problem has not identified girder specifications.


So the total DC for the slab:


                   



Now that you already have determine the dead loads, you can convert such loads to moment using any method you are familiar with for indeterminate structures (moment distribution, three moment equation, slope deflection method)

For the uniformly distributed load:

For the parapet DC:

By using moment distribution, the resulting moment for DC total:

The moment for DW:

The moment for the parapet: (Note that at the location of max. moment for the distributed loads, the moment shown for the parapet = 0.92 kN/m.

The moment due to live load is computed from the table:

By interpolation, compute for the positive moment of S=2650.

Moment due to LL = 27670 N

Finally, we can compute for the positive moment of the bridge from the formula: